Variational principles for spin systems and the Kirchhoff rod
François Gay-Balma - Control and Dynamical Systems, California Institute of Technology, Pasadena, CA 911125, United States (email)
Abstract: We obtain the affine Euler-Poincaré equations by standard Lagrangian reduction and deduce the associated Clebsch-constrained variational principle. These results are illustrated in deriving the equations of motion for continuum spin systems and Kirchhoff's rod, where they provide a unified geometric interpretation.
Keywords: variational principles, symmetry, Lagrangian reducton, cocycle, affine Euler-Poincaré equations, spin system, Kirchhoff rod.
Received: April 2009; Revised: July 2009; Available Online: January 2010.
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